List questions from group-isomorphism

Published on 25 Mar 2026 - 9:49

175

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Are the two groups $\mathbb R$ and $\mathbb C$ isomorphic?

Published on 08 May 2020 - 4:41

35

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isomorphisms - subgroup of an specific order (prove)

Published on 01 Apr 2026 - 2:40

144

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Isometric isomorphism between Hardy Space $h^p(\mathbb{D})$ and $L^p(\mathbb{T})$

Published on 26 Mar 2026 - 6:25

123

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The datum of a group is strictly more than the datum of a group up to isomorphism

Published on 11 May 2020 - 19:58

56

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Can we find a field, if we have a group?

Published on 13 May 2020 - 8:55

2.7k

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Show that $\mathbb{Z}[x]/(x)$ is isomorphic to $\mathbb{Z}$

Published on 13 May 2020 - 15:51

484

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Showing that $\mathbb{Z}[x]/_{(x)}$ is isomorphic to $\mathbb{Z}$

Published on 13 May 2020 - 17:29

61

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Prove that $M_{16} / Z(M_{16}) \cong C_2 \times C_2$

Published on 26 Mar 2026 - 11:17

226

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Why is it so computationally hard to determine group isomorphism?

Published on 25 Mar 2026 - 6:27

59

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First isomorphism theorem $G=\mathbb{Z}/60\mathbb{Z}=<\overline{1}>$

Published on 16 May 2020 - 8:55

41

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Do isomorphisms of quotients give isomorphisms of groups?

Published on 18 May 2020 - 14:42

253

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Showing this quotient group is isomorphic to $\mathbb{Z}_2\times{}\mathbb{Z}_2$

Published on 26 Mar 2026 - 16:06

470

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Is Aut(G×H) isomorphic to Aut(G) × Aut(H)

Published on 26 Mar 2026 - 17:35

193

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Show $G\cong \ker(f) \times \mathbb{Z}$ for abelian $G$

Published on 28 Mar 2026 - 13:02

List Question

Prove that $G(\mathbb{Q}(\zeta)/\mathbb{Q}) $ and $\mathbb{Z}_n^\times$ are Isomorphic

Are the two groups $\mathbb R$ and $\mathbb C$ isomorphic?

isomorphisms - subgroup of an specific order (prove)

Isometric isomorphism between Hardy Space $h^p(\mathbb{D})$ and $L^p(\mathbb{T})$

The datum of a group is strictly more than the datum of a group up to isomorphism

Can we find a field, if we have a group?

Show that $\mathbb{Z}[x]/(x)$ is isomorphic to $\mathbb{Z}$

Showing that $\mathbb{Z}[x]/_{(x)}$ is isomorphic to $\mathbb{Z}$

Prove that $M_{16} / Z(M_{16}) \cong C_2 \times C_2$

Why is it so computationally hard to determine group isomorphism?

First isomorphism theorem $G=\mathbb{Z}/60\mathbb{Z}=<\overline{1}>$

Do isomorphisms of quotients give isomorphisms of groups?

Showing this quotient group is isomorphic to $\mathbb{Z}_2\times{}\mathbb{Z}_2$

Is Aut(G×H) isomorphic to Aut(G) × Aut(H)

Show $G\cong \ker(f) \times \mathbb{Z}$ for abelian $G$

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